Electromechanical coupling in kinetic energy harvesters is the key aspect of these devices that ensures an effective energy conversion process. When modelling and designing such devices, it is necessary to incorporate electromechanical coupling correctly since it will determine the amount of energy that will be converted during its operation. As the engineering community prefers compact (lumped) models of such devices, the conventional choice of the lumped model for the electromagnetic type of electromechanical coupling is linear damping, proportional to the velocity of the mechanical resonator in a harvester, leading to the idea of maximizing the velocity in order to improve the energy conversion process. In this paper, we show that electromechanical coupling in electromagnetic kinetic energy harvesters is inherently nonlinear and requires a number of aspects to be taken into account if one wants to optimize a device. We show that the proposed model, which is based on first principles of electromagnetics, can be reduced to a nonlinear lumped model that is particularly convenient for analysis and design. The modelling approach and the resulting lumped model are verified using two MEMS electromagnetic harvesters operating over a range of frequencies from 300 to 500 Hz (Harvester A) and from 50 to 70 Hz (Harvester B) generating from mV (Harvester A) to few volts (Harvester B) of RMS voltage, respectively. The proposed modelling approach is not limited to energy harvesters but can also be applied to magnetic sensors or other MEMS devices that utilise electromagnetic transduction.